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ST371 Midterm I Practice Name The following are some additional practice problems to help you prepare for the midterm exam Note this is not a practice exam and this does not necessarily represent an exhaustive list of the concepts we have covered 1 Starting at a fixed time each car entering an intersection is observed to see whether it turns left L right R or goes straight ahead A The experiment terminates as soon as a car is observed to turn left Let X be the number of cars observed What are possible X values List five outcomes of this experiment and their associated X values 2 A contractor is required by a county planning department to submit one two three four or five forms depending on the nature of the project in applying for a building permit Let Y be the number of forms required of the next applicant The probability that y forms are required is known to be proportional to y that is p y ky for y 1 5 a What is the appropriate value of k b What is the probability that at most 3 forms are required c Could p y y2 50 for y 1 5 be the pmf of Y Explain 3 A library subscribes to two different weekly news magazines each of which is supposed to arrive in Wednesday s mail In actuality each one may arrive on Wednesday Thursday Friday or Saturday Suppose the two arrive independently of one another and for each one P Wed 3 P Thurs 4 P Fri 2 and P Sat 1 Let Y be the number of days beyond Wednesday that it takes for both magazines to arrive so possible values of Y are 0 1 2 or 3 Compute the pmf of Y 4 For customers purchasing a refrigerator at a certain applicance store let A be the event that the refrig erator was manufactured in the U S B be the event that the refrigerator had an icemaker and C be the event that the customer purchased an extended warranty Suppose we know P A 75 P B A 9 P B A 8 P C A B 8 P C A B 6 P C A B 7 P C A B 3 a What is the probability the customer bought a refrigerator with an icemaker with the extended warranty that was made in the U S b What is the probability the customer bought a refrigerator with an icemaker with the extended warranty c What is the probability the customer bought the extended warranty d If the customer bought a refrigerator with an icemaker with the extended warranty what is the probability the refrigerator was made in the U S

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